Random Walks in Electric Networks

  • D. M. L. D. Rasteiro
Conference paper
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 61)


The problem considered is the optimization of the value of a certain utility function defined over a general resistor random network. A probabilistic interpretation to the qualities in electric network will be given. To the network arcs there are associated parameters which represent the time/length/probability that an object takes to travel from a node into another. Starting from a source node, one wants to determine the optimal path to a sink node that optimizes the value of the utility function. Using network optimization it will be determine the network path which as the smallest resistance (highest conductance).


Optimal paths Probabilities Probable location of an object inside a network 


  1. 1.
    Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows theory, algorithms, and applications. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar
  2. 2.
    Bard JF, Bennett JE (1991) Arc reduction and path preference in stochastic acyclic networks. Manag Sci 31(7):198–215CrossRefGoogle Scholar
  3. 3.
    Bellman R (1958) On a routing problem. Q Appl Math 16:88–90Google Scholar
  4. 4.
    Cheung RK, Muralidharan B (1995) Dynamic routing of priority shipments on a less-than truckload service network. Technical report. Department of Industrial and Manufacturing Systems Engineering, Lowa State UniversityGoogle Scholar
  5. 5.
    Luce RD, Raiffa H (1957) Games and decisions. Wiley, New YorkzbMATHGoogle Scholar
  6. 6.
    Rasteiro DMLD (2008) Finding optimal paths in networks where arc parameters are not deterministic. In: Putnik GD, Cunha MM (eds) Encyclopedia of networked and virtual organizations. Information Science Reference, Hershey, pp 1151–1163. doi:  10.4018/978-1-59904-885-7.ch151
  7. 7.
    Rasteiro DDML, Anjo AJB (2004) Optimal paths in probabilistic networks. J Math Sci 120(1): 974–987. Springer, New York. ISSN: 1072–3374Google Scholar
  8. 8.
    Savage LJ (1954) The foundations of statistics. Wiley, New YorkzbMATHGoogle Scholar
  9. 9.
    von Neumann J, Mogenstern O (1947) Theory of games and economic behavior. Princeton University Press, PrincetonzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Mathematics and Physics DepartmentCoimbra Superior Engineering InstituteCoimbraPortugal

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